Analysis of Inner-Scale Effect on Atmosphere Scintillation for Infrared Laser Beam Propagating on Earth-Space Paths

On Earth-space paths, based on ITU-R C_n² (h) model, by means of a modification of the Rytov method that incorporates an amplitude spatial frequency filter function under strong fluctuation conditions, considering atmospheric turbulence inner-scale, an expression is developed for the scintillation index of a visible or a near and middle infrared laser beam wave that is valid under moderate to strong irradiance fluctuations. The quantitative analyses of scintillation index are done by this analytic model for laser Gaussian collimated beam wave at visible or near and middle infrared wave band. The results agree with theoretic analysis scintillation. This scintillation model can be converted into a Gaussian beam wave model with finite inner-scale on horizontal sight paths of invariable C_n².     

Scintillation of a laser beam propagation through non-Kolmogorov strong turbulence

Atmospheric turbulence causes strong irradiance fluctuations of propagating optical wave under the severe weather conditions in long-distance free space optical communication. In this paper, the scintillation index for a Gaussian beam wave propagation through non-Kolmogorov turbulent atmosphere is derived in strong fluctuation regime, using non-Kolmogorov spectrum with a generalized power law exponent and the extended Rytov theory with a modified spatial filter function. The analytic expressions are obtained and then used to analyze the effect of power law, refractive-index structure parameter, propagation distance, phase radius of curvature, beam width and wavelength on scintillation index of Gaussian beam under the strong atmospheric turbulence. It shows that, with the increasing of structure parameter or propagation distance, scintillation index increases sharply up to the peak point and then decreases gradually toward unity at rates depending on power law. And there exist optimal value of radius of curvature and beam width for minimizing the value of scintillation index and long wavelength for mitigating the effect of non-Kolmogorov strong turbulence on link performance.     

Scintillation index of optical wave propagating in turbulent atmosphere

A concise expression of the scintillation index is proposed for a plane optical wave and a spherical optical wave both propagating in a turbulent atmosphere with a zero inner scale and a finite inner scale under an arbitrary fluctuation condition. The expression is based on both the results in the Rytov approximation under a weak fluctuation condition and the numerical results in a strong fluctuation regime. The maximum value of the scintillation index and its corresponding Rytov index are evaluated. These quantities are affected by the ratio of the turbulence inner scale to the Fresnel size.     

湍流折射率谱型对大气闪烁和相位起伏功率谱的影响

基于Taylor湍流冻结假设理论,在不同湍流折射率谱型条件下,推导得出了光波闪烁和相位起伏频谱的表达式;数值计算了湍流谱型中折射率标度指数、内尺度以及外尺度变化时对光波频谱的影响。结果表明:随着折射率起伏标度指数的增大,闪烁频谱的低频段不再仅为常数,高频段下降的幂率逐渐增大,同时相位频谱在整个起伏频率段下降的幂率越来越大;湍流内尺度的增加将引起光波频谱的高频段下降的幂率越来越大;而随外尺度的减小,闪烁频谱低频段的振幅减小,这种影响在大口径接收时较为明显,相位谱的低频段幂率减小。     

实际大气中激光强度起伏的全年统计特征

对实际湍流大气中的激光强度起伏了系统的实验观测,详细分析了光强起伏的强度概率密度分布与功率谱的统计特征及春周日,全年变化规律。同时分析了探测器件的饱和铲应结果的影响。     

Study of Scintillation for Infrared Laser Beam Propagating in Atmospheric Turbulence on Earth-Space Paths

On earth-space paths, by applying a modification of the Rytov method that incorporates spatial frequency filter function under strong atmosphere fluctuation conditions, a tractable model is developed for the scintillation index of infrared laser Gaussian beam wave that is valid under moderate-to-strong irradiance fluctuations. At Infrared band, based on ITU-R C ² _n model, the scintillation indexes for collimation laser beam are predicted by this analytic model. The results agree with theoretic expected scintillation. This scintillation model can be converted into a plane or a sphere wave scintillation index model on earth-space paths, and also reduced to a Gaussian beam wave model on horizontal sight paths of invariable C ² _n.     

Theory of optical scintillation: Gaussian-beam wave model

Abstract

A scintillation model previously developed by the authors is extended in this paper to the case of a propagating Gaussian-beam wave. As in the previous model, we account for the loss of spatial coherence as the optical wave propagates through atmospheric turbulence by eliminating effects of certain turbulent scale sizes that exist between the scale size of the spatial coherence radius of the beam and that of the scattering disc. These mid-range scale-size effects are eliminated through the formal introduction of spatial frequency filters that continually adjust spatial cut-off frequencies as the optical wave propagates. Unlike the previous model, in this paper we include the effect of a finite outer scale in addition to the inner scale. With a finite outer scale, the scintillation index can be substantially lower in strong turbulence than that predicted by a model with an infinite outer scale. This particular behaviour of scintillation in strong turbulence, mostly associated with horizontal paths near the ground, cannot be explained on the basis of previous expressions deduced from the asymptotic theory. Comparisons of the scintillation models with published experimental and simulation data through weak and strong irradiance fluctuations show excellent fits.     

General optical scintillation in turbulent atmosphere

A general expression of the scintillation index is proposed for optical wave propagating in turbulent atmosphere under arbitrary fluctuation conditions. The expression depends on extreme behaviors of the scintillation indices under both weak and strong fluctuations. The maximum scintillation index in the onset region and the corresponding Rytov index can be evaluated from the general expression. Plane and spherical waves in the cases of zero and non-zero turbulence inner scale are given as examples for illustration of the general behaviors of scintillation indices.     

Expressions of the scintillation index for optical waves propagating through weak non-Kolmogorov turbulence based on the generalized atmospheric spectral model

The high frequency “bump” which occurs in the turbulence spectral model just prior to the turbulence cell dissipation is important for the analysis of the irradiance scintillation for optical wave propagating through atmospheric turbulence. In this study, expressions of the irradiance scintillation index are developed from the generalized modified atmospheric spectral model for optical waves propagating through weak non-Kolmogorov turbulence. Compared with the expressions of the irradiance scintillation index derived from the general non-Kolmogorov spectral model, the new expressions can consider the influences of finite turbulence inner and outer scales and the influence of finite diameter aperture receiver. As the irradiance scintillation is caused mainly by the small scale turbulence cells' diffractive effects for weak turbulence, the turbulence outer scale's influence can be ignored. Numerical simulations show that variable inner scale values produce obvious effects on the irradiance scintillation for non-Kolmogorov turbulence.     

湍流大气中光波闪烁的圆环孔径平均因子

利用弱起伏条件下球面波在大气湍流中传输的光强起伏(闪烁)理论和圆环孔径滤波函数,获得了圆环孔径平均因子的精确表达式。将圆环孔径平均因子关于一个无量纲参量(孔径半径与菲涅耳尺度的比值)拟合成2阶多项式,再找出多项式系数与孔径内外径之比的函数关系,获得了圆环孔径平均因子关于该参量和孔径内外径之比的函数关系式。通过误差分析确定了拟合关系式的适用范围,在此范围内,拟合式与精确式的相对误差小于25%。分别用Tatarskii谱和修正Hill谱分析了湍流内尺度对圆环孔径平均因子的影响,结果显示:在其他条件不变的情况下,内尺度越大,孔径平均效应相对越小。     

大气湍流尺度对部分相干光传输特性的影响

本文在考虑湍流内外尺度的情况下,对部分相干高斯谢尔模型光束在大气湍流中的传输特性进行了研究.主要采用考虑湍流内外尺度的修正Von Karmon谱模型,推导了部分相干光在大气湍流中的平均光强分布、光束扩展均方根束宽和漂移方差的解析式.对比分析了不同湍流强度情况下,湍流内外尺度对部分相干光在大气湍流中水平和斜程路径上传输特性的影响.结果表明:相同条件下,光束在大气湍流中传输时,沿斜程传输时的抗湍流能力强于水平传输;相比于大气湍流内尺度,大气湍流外尺度对光束漂移影响较大,外尺度对光束扩展与光强分布的影响较小,当湍流外尺度增大时,漂移现象会越来越严重;相比于大气湍流外尺度,湍流内尺度对光束扩展与光强分布的影响较大,当内尺度减小时,光束扩展现象越来越严重,光强分布也更分散,内尺度对漂移几乎无影响.     

Irradiance scintillation considering finite turbulence inner scale for optical wave propagating through weak non-Kolmogorov turbulence

The turbulence inner scale plays an important role in investigating the irradiance scintillation index for optical wave propagating through atmospheric turbulence. However, previous expressions of the irradiance scintillation index, which were derived based on the general non-Kolmogorov spectral model, did not consider the influences of finite turbulence inner scale. In this study, based on the generalized exponential spectral model for non-Kolmogorov atmospheric turbulence, theoretical expressions of the irradiance scintillation index are derived for plane and spherical optical waves propagating through weak turbulence. The new expressions have considered the influences of the finite turbulence inner scale and the receiver aperture on the irradiance scintillation index. Numerical simulations are performed to analyze these parameters’ influences.     

激光在湍流大气中传输的闪烁系数及其测量

 理论研究了激光光束经过湍流大气后闪烁系数的变化规律,以ARM7的嵌入式系统构建数据采集模块,在采集激光光强因为大气湍流影响而变化的数据的基础上对存储的数据使用闪烁系数数学模型进行运算,运算结果通过网络传输,由PC端的界面显示变化曲线,从而了构造一个可以感测大气湍流的远程探测系统。用转动的相位板模拟湍流大气,利用所开发的测试系统测量激光光束通过湍流大气后的闪烁系数。实验结果显示高斯光束在湍流大气中的闪烁系数随传输距离的增加而增大,与理论模拟结果基本相符。由此可见该系统工作可靠稳定,可实时测量激光光束经过湍流大气的闪烁系数。     

Scintillation properties of dark hollow beams in a weak turbulent atmosphere

The on-axis scintillation index for a circular dark hollow beam (DHB) propagating in a weak turbulent atmosphere is formulated, and the scintillation properties of a DHB are investigated in detail. The scintillation index for a DHB reduces to the scintillation index for a Gaussian beam, an annular beam and a flat-topped beam under certain conditions. It is found that the scintillation index of a DHB is closely related to the beam parameters and can be lower than that of a Gaussian beam, an annular beam and a flat-topped beam in a weak turbulent atmosphere at smaller waist sizes and longer propagation lengths. PACS 42.25.Bs; 42.68.Ay     

Scintillation index of elliptical Gaussian beam in turbulent atmosphere

A tensor method is used to formulate the on-axis scintillation index for an elliptical Gaussian beam (EGB; astigmatic Gaussian beam) propagating in a weak turbulent atmosphere. Variations of the on-axis scintillation of an EGB are studied. It is interesting to find that the scintillation index of an EGB can be smaller than that of a circular Gaussian beam in a weakly turbulent atmosphere under certain conditions and is closely related to the ratio of the beam waist size along the long axis to that along the short axis of the EGB, the wavelength, and the structure constant of the turbulent atmosphere.     

激光大气闪烁的间歇特征

 以小波变换法观察了湍流大气中激光光强起伏的间歇特征, 并用奇性测度进行了定量的描述。根据间歇性参量的周日变化规律发现：激光大气闪烁的间歇性存在于所有的时间和起伏条件下,并且保持稳定,间歇性参量约为0.1,基本不随起伏条件和时间变化。     

The wave structure function in weak to strong fluctuations: an analytic model based on heuristic theory

The Rytov perturbation method can be used to derive analytic expressions governing statistical quantities of an optical wave propagating through the Earth's atmosphere. It is generally accepted that the validity of these expressions is restricted to the weak fluctuation regime, and that the wave structure function for plane and spherical waves obtained via the Rytov method is valid in all fluctuation regimes, for sufficiently small separation distances. Data from experimental results for the wave structure function as a function of the fluctuation strength for a fixed value of the separation distance indicate that the Rytov method does not accurately model the behaviour of the wave structure function in moderate to strong fluctuation regimes. This is similar to what is observed for the scintillation index. Recently, however, it was shown that the integral definition of the scintillation index obtained via the Rytov perturbation yields analytic expressions that are valid in all fluctuation regimes when a filter function is applied to the atmospheric spectrum. The underlying physical theory is that as the wave propagates, intermediate refractive index scale sizes fail to refract or diffract the beam. Hence, these scale sizes do not contribute to the scintillation index. In this paper, we investigate the results of applying this concept to the wave structure function. Specifically, we apply a filter function to the atmospheric spectrum and develop analytic expressions for the wave structure function for plane, spherical and Gaussian beam waves using the Rytov perturbation method. It is shown that in weak fluctuations these expressions yield similar results to standard expressions obtained where no filter function is applied. However, in moderate to strong fluctuations, these new expressions predict a decrease in the value of the wave structure function as compared to the standard expressions, following the trend of the experimental data presented by Gurvich.

(Some figures in this article are in colour only in the electronic version)     

利用闪烁和漂移效应测量大气折射率结构常数的对比分析

 在近海面大气边界层中进行了1 km路径的水平光传输实验,结果表明：利用闪烁和漂移效应推导的大气折射率结构常数之间存在着较大的差异。定量的理论分析揭示了两者不一致的原因在于：闪烁效应主要对路径中部的小尺度湍涡敏感,漂移效应则对发射端附近的大尺度湍涡敏感;随着内尺度变大,漂移效应测量的折射率结构常数将大于闪烁效应测量的折射率结构常数,当内尺度达到20 mm时,前者的测量结果是后者的3倍;当外尺度变小时,漂移效应的测量结果小于闪烁效应的测量结果,当外尺度仅为1 m时,前者的测量结果为后者的1/2;大气折射率3维功率谱的幂律的变化对测量结果的影响非常大,当幂律大于-11/3时,闪烁效应测量的折射率结构常数大于漂移效应测量的折射率结构常数, 最大差异接近于25倍, 当幂律小于-11/3时,漂移效应的测量结果大于闪烁效应的测量结果,两者的差异甚至可达两个量级。     

复杂传播路径条件下激光光强起伏特性研究

对复杂地形情况下实际湍流大气中的激光强度起伏进行了系统的实验观测,分析了光强起伏统计特征的周日及全年变化规律。结果发现：复杂地形情况下实际湍流大气中的激光光强起伏,不论是概率密度分布还是其功率谱等统计特征均与理论上的偏离很大。     

高斯波束在湍流大气斜程传输中的闪烁问题研究

根据光波斜程传输理论以及随高度变化的ITU-R湍流大气结构常数模型,将水平传输的修正里托夫方法推广到了斜程传输问题中。导出了高斯波束入射时,在零内尺度湍流谱模型及考虑湍流内尺度效应和外尺度效应条件下,从弱起伏湍流区到强起伏湍流区闪烁指数随斜程里托夫方差变化的计算公式。讨论了不同传播高度、不同湍流内、外尺度对高斯波束斜程传输闪烁指数的影响。最后将有关数值计算结果与实验测量结果进行了比较和验证。